I think this article by Robyn Pennacchia comes closest to explaining Peterson’s appeal. There are a lot of meaty quotes in there if you want to see the evidence, including a great summary of his bogus transgender pronoun complaint, but the conclusion is excellent.
Peterson is telling young men the story they want to hear about themselves and the world around them. That they are “individuals,” that hierarchy and inequality are not bad things, that we live and have always lived in a meritocracy. That people aren’t clamoring for equality because they are good people who want people to be treated fairly and decently, but because they want to manipulate them and put them in gulags. That women are going to be just fine with jumping back into “traditional” gender roles and give them their patriarchy back. That women will not be put off by misogyny. That soon they will be living in a world where they can insult people — and yes, refusing to use someone’s preferred pronoun is insulting to them — and there will be no social consequences for that. That, rather than having enjoyed unearned privileges and advantages, those who have risen to the top of our societal hierarchy did so because they were simply the hardest and best workers. Because they were simply lobsters with more serotonin.
It’s an overly simplistic — and often intentionally vague — worldview that intellectualizes the basest id impulses of men, largely white men, who feel that they have been disadvantaged by the recent successes of white women and people of color and now feel left behind. He tells them they are logical, rational, critical thinkers — heroes, in fact. Even by doing things like talking a lot about the importance of IQ, he sates their desires to feel important and special. Take a moment and think of all the men you’ve ever met who were not doing much with their lives but very much wanted to talk to you about how high their IQ is (even though that’s ridiculous because most people probably don’t even know their actual IQ, for a variety of reasons). This is a thing. He doesn’t have to tell them they have a high IQ (because everyone thinks they have a high IQ), he just has to talk about how it is important, and that makes them feel good.
The thing is, he’s promising these men a world they actually cannot have without the permission of other groups of people. He’s not doing them any favors. If he really wanted to help these “lost men,” he’d help them thrive in the actual world they live in, rather than the way they want the world to be. He’d help them learn to adjust to a world in which the old hierarchies have been dismantled and understand that they’re no more entitled to be at the top of a hierarchy than anyone else is. Or help them learn how to function and love and improve themselves without needing to base that on being “better” than someone else, how to deal with the world in which women don’t want traditional gender roles, and help them to understand that life isn’t a zero sum game in which if someone who has been oppressed gets a right you have, you automatically lose something.
That last paragraph is familiar. It’s the same thing feminists have been saying to men, that everyone has been saying to MRAs, for years: the patriarchy is not your friend. A hierarchy that puts undeserving white men at the top does no one any favors. It’s almost a Petersonian thing to say, that if you want respect, you have to straighten up and earn it…and it’s ironic that his career is all about promising the opposite, that if you’ve got status, you must have deserved it, so don’t let women and minorities make you work for it.